In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every almost inner derivation of a complex nilpotent Leibniz algebra with one-dimensional commutator ideal, with three exceptions, is an inner derivation.
La Rosa, G., Mancini, M. (2023). Derivations of two-step nilpotent algebras. COMMUNICATIONS IN ALGEBRA, 51(12), 4928-4948 [10.1080/00927872.2023.2222415].
Derivations of two-step nilpotent algebras
La Rosa, Gianmarco;Mancini, Manuel
2023-01-01
Abstract
In this paper we study the Lie algebras of derivations of two-step nilpotent algebras. We obtain a class of Lie algebras with trivial center and abelian ideal of inner derivations. Among these, the relations between the complex and the real case of the indecomposable Heisenberg Leibniz algebras are thoroughly described. Finally we show that every almost inner derivation of a complex nilpotent Leibniz algebra with one-dimensional commutator ideal, with three exceptions, is an inner derivation.
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